A Central Limit Theorem for the average target hitting time for a random walk on a random graph

Abstract

Consider a simple random walk on a realization of an Erdős-Rényi graph. Assume that it is asymptotically almost surely (a.a.s.) connected. Conditional on an eigenvector delocalization conjecture, we prove a Central Limit Theorem (CLT) for the average target hitting time. By the latter we mean the expected time it takes the random walk on average to first hit a vertex $j$ when starting in a fixed vertex $i$. The average is taken with respect to ${\pi }_i$, the invariant measure of the random walk.